When Enrique Peña Nieto was a candidate in Mexico's presidential elections, allegations that he had benefited from favourable media coverage triggered mass student demonstrations against him and his party. When he won the 1 July election, those allegations formed part of a legal challenge to his victory.

Now, as the young and telegenic president-elect from the Institutional Revolutionary party, or PRI, prepares to take charge of the country on 1 December, the media allegations have been deemed legally irrelevant – and the furore they once caused has all but died away.

The runner-up, Andrés Manuel López Obrador, and his party of Democratic Revolution, or PRD, were unable to persuade Mexico's federal electoral tribunal that there had been unfair favourable coverage of Peña Nieto, alongside other allegations such as massive vote buying and dubious campaign funding, such as to violate constitutional guarantees that elections be "authentic and fair".

The part of the tribunal's unanimous decision on 30 August that referred to media bias drew heavily on an earlier decision by the Federal Electoral Institute, or IFE. That decision threw out a specific PRD complaint about "hidden publicity" by Peña Nieto, particularly on TV channels and other outlets associated with the broadcasting giant Televisa.

"They were unable to demonstrate that the role of Televisa was illegal," said the media expert Raul Trejo. "The case is closed. Some people might question the [legal] rules, but these are the rules we have."

Only one of the nine members of the IFE general council, which considered the "hidden publicity" complaint in a publicly broadcast debate on 16 August, voted against a "proposal" put before it by the institution's investigative branch.

The proposal rubbished the quality of the evidence submitted by the PRD, which relied heavily on journalistic accounts of the alleged bias, among them an article published in the Guardian on 7 June.

The article was based on a cache of documents dated from 2005 appearing to show promotional packages, including coverage on Televisa, drawn up for political clients, including Peña Nieto when he was just taking over as governor of the state of Mexico. Televisa has challenged the authenticity of these documents, and has denied it sold favourable news coverage to politicians including Peña Nieto.

The full IFE proposal described the Guardian article as "a subjective evaluation that is based on events than cannot be verified". However, the debate in the IFE general council on 16 August automatically ruled out consideration of this and other evidence presented by the PRD that referred to alleged misconduct prior to 2007/8 legal reforms that drastically tightened restrictions on TV and radio advertising.

It also dismissed the relevance of events already considered in previous rulings, such as a 2011 case in which the electoral authorities had sanctioned both Televisa and Mexico's other national network, TV Azteca, for transmitting political advertisements promoting governor Peña Nieto around the country. The law says such advertisements should only be broadcast locally.

The most eye-catching allegation admitted for consideration was that the Peña Nieto campaign had paid for an interview in April on a radio show presented by a celebrity journalist, which was deemed groundless.

Most of the debate in the IFE general council, however, focused on the question of whether the investigation into the evidence presented by the PRD had gone far enough. Alfredo Figueroa, the only member to vote against the proposal, argued that it had been superficial. He said it should have included more in-depth probing, including a requirement that prominent news anchors answer questions derived from the allegations.

Another council member, Lorenzo Cordova, partially backed this position. He qualified his vote in favour of the proposal by stating that a "richer investigation" might have produced a different result.

The overwhelming majority view, however, insisted that there was nothing in the complaint to justify "additional irritation" to journalists and media outlets featured in the evidence. A more exhaustive investigation, several of the council members said, would have violated guarantees of freedom of expression.

"The way that the alleged damages was argued, their relationship with events, and the temporality in which they occurred, led the investigation into a wall in all cases," the council member Benito Nacif said. "It was unnecessary to continue."

Both the IFE's decision, and the tribunal's subsequent wholesale dismissal of all other allegations of unfair play in the elections, sparked sharp criticism from some commentators as well as student protests. But the marches have since dwindled, as the movement appears to be running out of steam, and attention has refocused on what a Peña Nieto administration will actually look like, rather than how he is portrayed.

The media expert Trejo nevertheless insists that while the controversy over the alleged bias may have waned, it has left a legacy of concern about the ethical nature of the relationship between the media and politicians in general. At the height of the post-election conflict Peña Nieto said that setting up an independent body to keep an eye on publicity spending at all levels of government was one of his priorities. "This issue," Trejo said, "is here to stay".

In its recent final review of this year's presidential election, IFE concluded that Televisa's news coverage on its nationwide newscasts had been fairly divided between the three main presidential candidates, stating that by the close of campaigning each of them had received just over 42 hours of coverage.